The emergence of order in many element systems

TL;DR

This paper introduces a new concept called order in mean field models, emphasizing self-organization in systems, and demonstrates its applicability and propagation in the Choose the Leader model.

Contribution

It defines a novel asymptotic correlation relation called order, contrasting with chaos, and explores its emergence and propagation in mean field systems.

Findings

Order emerges as a form of self-organization in the model.

The new correlation relation applies to biological and societal systems.

Order propagates within the Choose the Leader model.

Abstract

Our work is dedicated to the introduction and investigation of a new asymptotic correlation relation in the field of mean field models and limits. This new notion, order (as opposed to chaos), revolves around a tendency for self organisation in a given system and is expected to be observed in biological and societal models. Beyond the definition of this new notion, our work will show its applicability, and propagation, in the so-called Choose the Leader model.